SCRS/2007/109 Collect. Vol. Sci. Pap. ICCAT, 61(4): 1084-1087 (2008)
George Tserpes 1
SUMMARY
Biomass and MSY estimates for the Mediterranean swordfish stocks were obtained from a nonequilibrium surplus model approach which utilized standardized CPUE time series from commercial long-liners and fishery production data. Model estimates were made through open source code developed in “R-language” and results demonstrated the existence of fisheries over-exploitation. Stock biomass remains stable in the latest years at levels, however, lower than those corresponding to MSY benchmarks.
RÉSUMÉ
Les estimations de la biomasse et de la PME pour les stocks d’espadon de la Méditerranée ont été obtenues par une approche de modèle de production excédentaire en conditions de non-équilibre, utilisant les séries temporelles de la CPUE standardisée d’après les données de production de la pêcherie et des palangriers commerciaux. Les estimations du modèle ont été réalisées par un code source libre développé en “langage R ” et les résultats ont démontré l’existence d’une surexploitation des pêcheries. La biomasse du stock reste stable ces dernières années, se situant toutefois à des niveaux inférieurs à ceux correspondant aux points de référence de la PME.
RESUMEN
Se obtuvieron las estimaciones de biomasa y RMS para los stocks de pez espada del Mediterráneo a partir de un enfoque de modelo excedente en no equilibrio que utilizaba series temporales de CPUE estandarizada de los datos de producción de palangreros comerciales y de las pesquerías. Las estimaciones del modelo se realizaron a través de un código de fuente abierta desarrollado en
“lenguaje R” y los resultados demostraron la existencia de sobreexplotación en las pesquerías. La biomasa del stock permanece estable en los últimos años a niveles, no obstante, inferiores a los que corresponden a los valores de referencia del RMS.
KEYWORDS
Swordfish, Mediterranean, stock assessment
1. Introduction
The Mediterranean swordfish stock is heavily exploited by several countries that have fisheries targeting swordfish by means of surface long-lines and/or gillnets. Swordfish fishing is carried out throughout the year, but for most fisheries is more intensive from late spring to middle autumn (Anon. 2004). Overall catch levels are rather stable in the last decade and the latest ICCAT assessment suggested that the stock is in rather stable position in terms of fishing mortality and recruitment (Anon. 2004). However, the lack of sufficient historical data did not allow the determination of stock status relative to MSY benchmarks.
In the present work we attempt to provide assessment estimates for the stock, based on the logistic surplus production model (Schaefer 1954). We use a non-equilibrium approach which utilizes a time series of CPUE and fisheries production data.
1
Hellenic Centre for Marine Research, P.O Box 2214, 71003, Iraklion, Greece.
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2. Materials and methods
2.1 Data
The following data were used as input for the logistic model:
Total Mediterranean landing estimates by year for the period 1987-2005 extracted from ICCAT data base
A yearly index of standardized CPUE series for the above period (with the exception of the years 1989,
1996 and 1997) based on data from the Greek long-liners operating in the Eastern Mediterranean
(Tserpes et al.
in this volume)
Exploitation rate at the beginning of the studied period based on the mortality estimates of the latest
VPA assessment. Values of F and M for the beginning of the period were fixed to 0.40 and 0.20 respectively (Anon. 2004)
2.2 Modeling approach
It was assumed that population follows the logistic model of growth and estimates of model parameters were made assuming a non-equilibrium approach. In fact, we follow an observation error/time series fitting method which assumes that the underlying production relationship is correct, and that all the errors occur in the relationship between true stock size and the index used to measure it (Pella and Tomlinson 1969). Hence, the parameter values are adjusted to provide the best fit of the predicted to observed time series of relative abundance.
For a given r value the following approach has been followed:
1.
Estimation of harvest rate for the beginning of the period: hr

F
Z


1
 e

Z

2.
Estimation of initial biomass fraction (i.e. B/k): B fr

1
 hr r
3.
Estimation of a starting k value:
4.
Estimation of initial biomass: B
0 k in

C av

B fr

 r k in
4
(assumes that average catch is around to MSY).
5.
Estimation of a starting q value: q in

U av
( U av
=mean abundance index).
B
0
6.
Final estimates of model parameters (k, q) were obtained using a least squares criterion of fit assuming log-normal residual errors between the observed and expected abundance indices. The equations used were:
B t

B t

1
 rB t

1
( 1

B t

1
)

C t

1
, U t
 qB t
and
 t

(log U t
 log
^
U t
)
2 k
The above steps have been repeated for a series of consecutive r values (range 0.30-0.99, interval 0.01). As the best model, was considered that providing the lowest error and its parameters were used to calculate population biomass time series, equilibrium MSY and F msy
.
Model estimates were made by means of computer code developed in R-language.
3. Results
Based on the ICCAT VPA assessment the values of F and M for the beginning of the period were fixed to 0.40 and 0.20 respectively (Anon. 2004). The best fit was provided for r = 0.65 and k=89870 mt. Observed and predicted indices are shown in Figure 1 . Based on the above estimates equilibrium MSY was found to be equal to 14604 mt. The corresponding rates for fishing mortality and biomass are:
F msy
 r
2
 0 .
30 and
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B msy
 k
2
 47881 mt. Annual catches in the latest years are around to MSY , while stock biomass levels are stable but lower than B msy
( Figure 2 ).
4. Discussion
Results indicated that stock biomass is rather stable in the latest years, at levels however 10-12% lower than B msy.
This suggests the existence of an over-fishing situation. Recent catches are around to MSY but as equilibrium is assumed to be unlikely in a fished population, MSY should be rather interpreted as an average, long-term potential yield if the stock is fished optimally and not as an explicit target (Haddon, 2001). The fishery could be managed by limiting effort to achieve fishing mortality equal to F msy but since current biomass rates are under
B msy
a more conservative exploitation pattern is needed to allow stock rebuilding at optimum biomass levels. The
F
0.1 which is around to 90% of F msy
(Prager 1994) could be a reasonable target.
Taking into account that production data refer to the whole Mediterranean basin, utilization of CPUE data series from additional important Mediterranean fisheries (e.g. Italian, Spanish, Moroccan) would certainly improve the robustness of the above model parameter estimates.
Surplus production models and especially approaches that avoid equilibrium assumptions can provide useful guidance in fisheries and supplement estimates of age-based models. Monte-Carlo simulations have shown that observation-error techniques, such as the one followed in the current work, perform better than process-error methods (Polacheck et al.
1993). Observation-error methods demand subjective setting of B
0
and there are several approaches to determine B
0
, based on the characteristics of each fishery (Haddon 2001. In the present case B
0
determination was based on the reasonable assumption for a heavily exploited -but not depleted- fishery that average catch is around to MSY.
Preliminary trials with different B
0
values indicated that the above assumption resulted in the most conservative MSY estimates.
5. Acknowledgements
I would like to thank Dr. M. McAllister for useful suggestions regarding the application of the surplus production model.
References
ANON. 2004. ICCAT Mediterranean swordfish stock assessment session. Collect. Vol. Sci. Pap. ICCAT, 56(3):
789-837.
HADDON, M. 2001. Modelling and Quantitative Methods in Fisheries, Chapman & Hall.
PELLA, J.J. and P.K. Tomlinson. 1969. A generalized stock-production model. Bull. Int-Am. Trop. Tuna Com. 13:
421-458.
POLACHECK, T., R. Hilborn and A.E. Punt. 1993 Fitting surplus production models: Comparing methods and measuring uncertainty. Can. J. Fish. Aquat. Sci.: 50: 2597-2607.
PRAGER, M.H. 1994. A suite of extensions to a non-equilibrium surplus production model. Fishery Bulletin 92:
374-389.
SCHAEFER, M.B. 1954. Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull. Inter-Amer. Trop. Tuna Conmmission, 1: 27-56.
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Figure 1 . Observed abundance indices and model fitted line based on the predicted indices.
Figure 2.
Predicted stock biomass (black points) and observed catch by year (red points). Black and red horizontal lines indicate B
MSY
and MSY levels, respectively.
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